Question
Using the Power Rule of Exponents, what is an equivalent form of ((1/2)^10)^2?(1 point)%0D%0AResponses%0D%0A%0D%0A(12)(10⋅2)%0D%0Aleft parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript left parenthesis 10 times 2 right parenthesis baseline%0D%0A%0D%0A(12)(10−2)%0D%0Aleft parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript left parenthesis 10 minus 2 right parenthesis baseline%0D%0A%0D%0A(12)(10÷2)%0D%0Aleft parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript left parenthesis 10 divided by 2 right parenthesis baseline%0D%0A%0D%0A(12)(10+2)
Answers
GPT-4o mini
Using the Power Rule of Exponents, which states that \((a^m)^n = a^{m \cdot n}\), we can simplify \(((1/2)^{10})^2\) as follows:
\[
\left(\frac{1}{2}\right)^{10 \cdot 2} = \left(\frac{1}{2}\right)^{20}
\]
Thus, the correct response is:
\(\left( \frac{1}{2} \right)^{(10 \cdot 2)}\)
\[
\left(\frac{1}{2}\right)^{10 \cdot 2} = \left(\frac{1}{2}\right)^{20}
\]
Thus, the correct response is:
\(\left( \frac{1}{2} \right)^{(10 \cdot 2)}\)